writing the research report with explanations on the results
The statistical report below clearly describes all the findings of the underlying research. It begins by giving a brief summary of the processes and methods then proceeds to explain the model used to analyze the data obtained (regression model) after which it explains the obtained results.
Based on the results provided, what can you conclude about the degree to which institutional characteristics of Catholic colleges are related to students' perception of the school's religious identity? Write a report summarizing your conclusions.
We linked the response of each student to the institutional characteristics of the college or university he or she attended in order to answer the question, “To what extent do institutional characteristics of a school affect student perceptions of its religious identity?” Then, we ran a linear regression with student perception as the dependent variable and the full set of institutional characteristics as independent variables.
The results of the regression analysis based on the above paper (with slight modifications) are shown in the tables below. Use these results, along with the above context, to write your report.
Brief research summary
The research seeks to investigate the effect of institutional characteristics on a school students’ perception of its religious identity. In other to establish this relationship, over 1000 students were Surveyed across 26 different catholic colleges and universities, and data were gathered on their perceptions of their institutions' Catholic culture. Due to items non-response (missing values)of about136 students (12.4%), only 963 results of the survey were completed and reported making the total number of students surveyed equally to 1099. Regression analysis was employed in fitting a predictive model to this dataset taking students’ perception as the dependent Variable and full set of institutional characteristics such as Religious president, Alcoholpolicy, Coed dorms, Visitation policy, Daily mass, Sunday mass, Service learning, and Required catholic courses as independent Variables.
Explaining the regression coefficients
The regression coefficients in table3 contain intercept and coefficients for the eight explanatory variables. The intercept 1.679 is the expected value of the Students’ perception if all the predictors are held constant or zero. Two of the coefficients are negative(Religious president and Sunday mass) while the remaining six are positive. The negative coefficients of -0.018 &-0.027 imply that the value of Students ‘perception will decrease by 0.018 and 0.027 as a result of a unit change in Religious president and Sunday mass respectively. On the other hand, the positive coefficients of 0.015, 0.107, 0.212, 0.226, 0.084 &0.18 mean that the value of Students’ perception is expected to increase by this coefficient as a result of a unit change in Alcoholic policy, co-ed dorms, Visitation policy, Daily mass, and service-learning and Required catholic courses respectively.
Elaborating on the results of the regression analysis
The results of the regression analysis revealed that four of the explanatory variables (Co-ed dorms, Visitation policy, Daily mass, and Required catholic courses) are statistically significant at a 5% level of significance with p-values less than the significance value (0.05)while the remaining four variables are not significant statistically with p-values greater than the significance values (0.05). This implies that only the significant variables Co-ed dorms, Visitation policy, daily mass, and required catholic courses contribute significantly to the prediction of students’ perception.
Explaining ANOVA results in table 2
Table2 presents ANOVA for the regression model and this is helpful in assessing the overall performance of the model. F(8,954) = 36.67and P-value < 0.01, we reject the null hypothesis since the P-value is less than 5% and even 1% level of significance and conclude that the model is statistically significant and adequate for prediction.
The coefficient of determination reported in table1 is 0.235 and this implies that about 23.5% of the variation in students’ perception is jointly explained by all the explanatory variables in the model.
Assumptions of the linear regression model used
On the assumption of linear regression model which are Linearity, Normality of errors, Multicollinrarity, Homoscedasticity and Autocorrelation. Multicollinearity and Normality of errors need verification for the model as some of the Variables may be correlated which will present repetition of a variable in a model, Also, the dependent variable doesn’t seem normal, checking the Normality of errors will help in choosing the right distribution for the dependent variable. If the errors appear non-Gaussian, a generalized linear model will be preferred.
Demystifying the results
The surprising result of the model is the ANOVA table which shows a very low p-value implying higher significance even though four out of eight explanatory variables are not statistically significant. We expect the overall performance of the model to be fair since half of the variables are not significant but surprisingly, it’s very adequate and highly significant.
Student perceptions of Catholic identity are affected by their residential life and the presence of Catholic students on campus. Including these variables in the model will help improve and also explain it more.
In summary, regardless of an institution's curriculum and policies, students have a significant role in defining the institution's Catholic identity.